Deterministic Growth-Dispersal Models and Branching Random Walk

摘要

In 1982 H.F. Weinberger introduced a quite general deterministic evolution model, where time is discrete and space may be discrete or continuous. The case of continuous space, also called habitat, has been studied in more detail. Less is known in the case of discrete habitat, and this case will be the object of study in this paper. The main objective is to relate Weinberger's deterministic growth-dispersal model (DGD) to branching random walk (BRW) so that results from one of these fields will translate to the other. This attempt may be viewed as a discrete version of the well known relation between the Fisher (or KPP) equation and branching Brownian motion. (Copyright (c) 1993 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)